Solve for $n$, $ \dfrac{n + 7}{5n - 1} = \dfrac{3}{5n - 1} + \dfrac{8}{25n - 5} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5n - 1$ $5n - 1$ and $25n - 5$ The common denominator is $25n - 5$ To get $25n - 5$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{n + 7}{5n - 1} \times \dfrac{5}{5} = \dfrac{5n + 35}{25n - 5} $ To get $25n - 5$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{3}{5n - 1} \times \dfrac{5}{5} = \dfrac{15}{25n - 5} $ The denominator of the third term is already $25n - 5$ , so we don't need to change it. This give us: $ \dfrac{5n + 35}{25n - 5} = \dfrac{15}{25n - 5} + \dfrac{8}{25n - 5} $ If we multiply both sides of the equation by $25n - 5$ , we get: $ 5n + 35 = 15 + 8$ $ 5n + 35 = 23$ $ 5n = -12 $ $ n = -\dfrac{12}{5}$